System and method for electromagnet coil construction

ABSTRACT

A method of manufacturing electromagnet coils for use in a magnetic resonance imaging (MRI) system is provided. The electromagnet coils are located in a non-homogeneous external magnetic field. The method comprises forming a coil representation of a coil surface for the electromagnet coils; setting limits for performance metrics for the electromagnet coils including a magnetic field-shape metric and at least one of an external torque metric and an external force metric, the external torque metric and the external force metric based, respectively, at least in part on a torque and a force exerted on the electromagnet coil by the non-homogeneous external magnetic field; forming a performance functional, based on the coil representation and the performance metrics, for generating a current density pattern over the coil surface; optimizing the performance functional and generating a current density pattern based on the optimized performance functional; and obtaining coil windings.

FIELD OF THE INVENTION

The present invention relates generally to magnetic resonance imaging. More specifically, the present invention relates to the construction and operation of magnetic coils.

BACKGROUND OF THE INVENTION

Magnetic resonance imaging (MRI) is a major imaging technique used in medicine. MRI is capable of generating detailed images of soft tissues such as the brain, muscles and kidneys. Specific properties of the various compounds found inside tissues, such as water and/or fat, are used to generate images. When subjected to a strong magnetic field, the vector sum of the nuclear magnetic moments of a large number of atoms possessing a nuclear spin angular momentum, such as hydrogen, which is abundant in water and fat, will produce a net magnetic moment in alignment with the externally applied field. The resultant net magnetic moment can furthermore precess with a well-defined frequency that is proportional to the applied magnetic field. After excitation by radio frequency pulses, the net magnetization will generate a signal that can be detected.

Various electromagnets are integral parts of an MRI system. For example, they allow spatial encoding of the detected signals for the formation of spatial images, and correction of any irregularities. Electromagnets perform this function by generating magnetic fields with predetermined shapes. For example, gradient coils are typically designed to generate magnetic fields that vary linearly with a constant tangent along the three perpendicular axis of the MRI systems' imaging volume.

Manufacturing electromagnets which can generate magnetic fields with the desired requirements such as desired magnetic field shapes can present challenges. Specifically, to function properly, electromagnets are typically produced to operate in accordance with additional requirements besides magnetic field shape. For example, it is desirable to produce gradient coils, which when energized have minimal net force and torque. This requirement is in addition to the linearity of the magnetic field produced.

Typically used methods of force and torque balancing for gradient coils, however, assume that the external magnetic field such as that produced by a main magnet of the MRI is a uniform magnetic field in space pointing in the axial (z) direction. When the external field is uniform, as long as current enters and exits the gradient coils at the same location, net forces on gradient coils (or other electromagnets) may not be produced. However, typically the external magnetic field to which gradient coils or other electromagnets are subjected is non-uniform in the region where a gradient coil or electromagnet is placed. For example, short superconducting magnets can have significant radial and axial non-uniformities in the magnetic field generated where the gradient coil is typically placed. Accordingly, a gradient coil may experience significant net forces and/or torque when placed in a non-uniform field, even if current enters and exits the gradient coils at the same location. Thus, improved electromagnet design, manufacturing and operating techniques are needed to allow the construction of electromagnets in accordance with specified requirements.

SUMMARY OF THE INVENTION

It is an object to provide a novel system and method for an MRI scanning system and method that obviates and mitigates at least one of the above-identified disadvantages of the prior art.

According to one aspect, a method of manufacturing electromagnet coils for use in a magnetic resonance imaging (MRI) system is provided. The electromagnet coils are located in a non-homogeneous external magnetic field. The method comprises: forming a coil representation of a coil surface for the electromagnet coils; setting a plurality of performance metric requirements for a plurality of performance metrics for the electromagnet coils, the plurality of performance metrics including a magnetic field-shape metric and at least one of an external torque metric and an external force metric, the external torque metric and the external force metric being based, respectively, at least in part on a torque and a force exerted on the electromagnet coil by the non-homogeneous external magnetic field; forming a performance functional, based on the coil representation and the performance metrics, for generating a current density pattern over the coil surface; optimizing the performance functional based on the performance metric requirements; generating a current density pattern over the coil surface based on the optimized performance functional; and obtaining coil windings for the electromagnet coils from the current density pattern.

These, together with other aspects and advantages which will be subsequently apparent, reside in the details of construction and operation as more fully hereinafter described and claimed, reference being had to the accompanying drawings forming a part hereof, wherein like numerals refer to like parts throughout.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 shows a block diagram of functional subsystems of a magnetic resonance imaging system in accordance with an implementation;

FIG. 2 shows an imaging volume and corresponding slice to be scanned by the magnetic resonance system of FIG. 1 in accordance with an implementation;

FIG. 3 shows an example pulse sequence in accordance with an implementation;

FIG. 4 shows a schematic representation of a k-space containing one received line in accordance with an implementation;

FIG. 5 shows a gradient coil wire pattern that is asymmetric along the longitudinal direction with one spiral per layer in accordance with an implementation.

FIG. 6 shows an example digitized cylindrical surface in accordance with an implementation;

FIG. 7 shows the example digitized cylindrical surface with a stream function pattern and a corresponding coil wire pattern in accordance with an implementation;

FIG. 8 shows an example non-homogeneous main magnetic field in accordance with an implementation; and

FIG. 9 shows a flowchart for a method of manufacturing gradient coils for use in the magnetic resonance imaging system of FIG. 1 in accordance with an implementation.

DETAILED DESCRIPTION

Referring to FIG. 1, a block diagram of a magnetic resonance imaging (MRI) system, in accordance with an example implementation, is shown at 100. The example implementation of the MRI system indicated at 100 is for illustrative purposes only, and variations including additional, fewer and/or varied components are possible. Traditional magnetic resonance imaging (MRI) systems represent an imaging modality which is primarily used to construct pictures of magnetic resonance (MR) signals from protons such as hydrogen atoms in an object. In medical MRI, typical signals of interest are MR signals from water and fat, the major hydrogen containing components of tissues.

As shown in FIG. 1, the illustrative MRI system 100 comprises a data processing system 105. The data processing system 105 can generally include one or more output devices such as a display, one or more input devices such as a keyboard and a mouse as well as one or more processors connected to a memory having volatile and persistent components. The data processing system 105 can further comprise one or more interfaces adapted for communication and data exchange with the hardware components of MRI system 100 used for performing a scan.

Continuing with FIG. 1, the example MRI system 100 can also include a main field magnet 110. The main field magnet 110 can be implemented as a permanent, superconducting or a resistive magnet, for example. Other magnet types, including hybrid magnets suitable for use in the MRI system 100 will now occur to a person of skill and are contemplated. The main field magnet 110 is operable to produce a substantially uniform main magnetic field having a strength B0 and a direction along an axis. The main magnetic field is used to create an imaging volume within which desired atomic nuclei, such as the protons in Hydrogen within water and fat, of an object are magnetically aligned in preparation for a scan. In some implementations, as in this example implementation, a main field control unit 115 in communication with data processing system 105 can be used for controlling the operation of the main field magnet 110.

The MRI system 100 can further include gradient coils, for example gradient coils 120 used for encoding spatial information in the main magnetic field along, for example, three perpendicular gradient axes. The size and configuration of the gradient coils 120 can be such that they produce a controlled and uniform linear gradient. For example, three paired orthogonal current-carrying primary coils located within the main field magnet 110 can be constructed to produce desired linear-gradient magnetic fields.

In some implementations, the gradient coils 120 may be shielded and include an outer layer of shield magnets, for example coils, which can produce a counter magnetic field to counter the gradient magnetic field produced by the primary gradient coils forming a primary-shield coils pair. In such a coil pair the “primary” coils can be responsible for creating the gradient field and the “shield” coils can be responsible for reducing the stray field of the primary coil outside a certain volume such as those external to the gradient coils 120. The primary-shield coils pair of the gradient coils 120, the primary and shield coils, may be connected in series. It is also possible to have more than two layers of coils for any given gradient axis that together form shielded gradient coils 120. The shielded gradient coils 120 may reduce eddy currents and other interference which can cause artefacts in the scanned images. Since eddy currents mainly flow in conducting components of the MRI system 100 and are caused by time-varying magnetic fields external to the gradient coils 120 (leakage fields), reducing the leakage fields produced by the gradient coils 120 may reduce interference. Accordingly, the shapes and sizes, conductor wire patterns and sizes, and current amplitudes and patterns of the primary-shield coils pair can be selected so that the net magnetic field outside the gradient coils 120 is as close to zero as possible. For cylindrical magnets, for example, the two coils can be arranged in the form of concentric cylinders whereas for vertical field magnets, the two coils may be arranged in coaxial disks.

One side effect of shielding can be that the fields produced by the primary-shield coils pair of the gradient coils 120 may partially cancel each other within the imaging volume. Accordingly, more current can be required to produce a gradient field with a particular strength by shielded gradient coils 120 than by unshielded gradient coils 120. This effect can be quantified as the gradient efficiency, which may be defined as the achievable gradient strength for 1 Ampere of driving current. Another important parameter describing gradient coil performance is called the gradient slew rate, which is the rate of driving a gradient coil from zero to its maximum amplitude. The maximum achievable slew rate is lower in gradient coils with greater inductance when driven with the same power amplifier. Typically, in order to increase the efficiency of a shielded gradient coils 120 to be comparable to the efficiency of an unshielded gradient coils 120 the inductance must increase. This increase in inductance will decrease the maximum achievable slew rate. The loss in efficiency for a shielded configuration can depend on the distance and current density ratio between the primary and shield coils. Increasing the distance between the primary-shield coils pair may increase the efficiency.

The conductive components of the gradient coils 120, whether shielded or unshielded and including the primary and shield coils, may consist of an electrical conductor (for example copper, aluminum, etc.). The internal electrical connections can be such that when a voltage difference is applied to the terminals of the gradient coils 120, electric current can flow in the desired path. The conductive components for the three gradient axes for both the primary gradient coils and the gradient shield coils can be insulated by physical separation and/or a non-conductive barrier. The primary gradient windings can be placed on a non-conductive substrate (for example, G10, FR4, epoxy or others).

In some variations, the gradient coils 120 may also be provided with thermal control or heat extraction mechanisms. For example, some of the windings can be hollow and coolant can be passed through these hollow conductors to extract heat from the gradient coils 120, produced, for instance, by resistive heating of the windings when electricity is applied. Alternatively, other methods of extracting heat can be used, such as inserting coolant channels within the gradient coils 120. The coolant channels can be in thermal contact with the gradient coil windings. The gradient coils 120 can also be mounted in a thermally-conductive but electrically-non-conductive epoxy to ensure that the mechanical assembly is rigid and to limit the possibility of electrical breakdown.

The magnetic fields produced by the gradient coils 120, in combination and/or sequentially, can be superimposed on the main magnetic field such that selective spatial excitation of objects within the imaging volume can occur. In addition to allowing spatial excitation, the gradient coils 120 can attach spatially specific frequency and phase information to the atomic nuclei placed within the imaging volume, allowing the resultant MR signal to be reconstructed into a useful image. A gradient coil control unit 125 in communication with the data processing system 105 can be used to control the operation of the gradient coils 120.

In some implementations of the MRI system 100, there may be additional electromagnet coils present, such as correction coils 140. The correction coils 140, which can include shim coils, a uniform field offset coil and any other corrective electromagnets, traditionally produce (but are not limited to) magnetic field profiles of 2nd order or higher spherical harmonics or uniform magnetic fields. To perform active correction or shimming (correcting the field distortions that are introduced when different objects are placed within or around the system), the corrective electromagnets, such as the correction coils 140, carry a current that is used to provide magnetic fields that act to make the main magnetic field more uniform. For example, the fields produced by these coils can aid in the correction of inhomogeneities in the main magnetic field due to imperfections in the main magnet 110, or to the presence of external ferromagnetic objects, or due to susceptibility differences of materials within the imaging region, or any other static or time-varying phenomena. A correction coil control unit 140 in communication with the data processing system 105 can be used to control the operation of the shim coils 140.

The MRI system 100 can further comprise radio frequency (RF) coils 130. The RF coils 130 are used to establish an RF magnetic field with a strength B1 to excite the atomic nuclei or “spins”. The RF coils 130 can also detect signals emitted from the “relaxing” spins within the object being imaged. Accordingly, the RF coils 130 can be in the form of separate transmit and receive coils or a combined transmit and receive coil with a switching mechanism for switching between transmit and receive modes.

The RF coils 130 can be implemented as surface coils, which are typically receive only coils and/or volume coils which can be receive and transmit coils. The RF coils 130 can be integrated near the main field magnet 110 bore. Alternatively, the RF coils 130 can be implemented in closer proximity to the object to be scanned, such as a head, and can take a shape that approximates the shape of the object, such as a close-fitting helmet. An RF coil control unit 135 in communication with the data processing system 100 can be used to control the operation of the RF coils 130.

There are many techniques for obtaining images using the MRI system 100, including T1 and T2 weighted images. To provide a simplified illustration of the MRI system 100's functionality, simplified operations for obtaining proton density-weighted images are described as a non-limiting example. To create an image in accordance with the example illustration, the MRI system 100 detects the presence of atomic nuclei containing spin angular momentum in an object, such as those of Hydrogen protons in water or fat found in tissues, by subjecting the object to a relatively large magnetic field. In this example implementation, the main magnetic field has a strength of B0 and the atomic nuclei containing spin angular momentum may be Hydrogen protons or simply protons. The main magnetic field partially polarizes the Hydrogen protons in the object placed in the imaging volume of the main magnet 110. The protons are then excited with appropriately tuned RF radiation, forming an RF magnetic field with a strength of B1, for example. Finally, weak RF radiation signal from the excited protons is detected as an MR signal, as the protons “relax” from the magnetic interaction. The frequency of the detected MR signal is proportional to the magnetic field to which they are subjected. Cross-sections of the object from which to obtain signals can be selected by producing a magnetic field gradient across the object so that magnetic field values of the main magnetic field can be varied along various locations in the object. Given that the signal frequency is proportional to the varied magnetic field created, the variations allow assigning a particular signal frequency and phase to a location in the object. Accordingly, sufficient information can be found in the obtained MR signals to construct a map of the object in terms of proton presence, which is the basis of a traditional MRI image. For example, since proton density varies with the type of tissue, tissue variations can be mapped as image contrast variations after the obtained signals are processed.

Referring now to FIG. 2, to further illustrate the example signal acquisition process by the MRI system 100, it will be assumed that an object is placed within an imaging volume 250 of the main magnet 110 having a main magnetic field 210 with a strength B0, pointing along the Z-axis indicated at 240. The object subsequently has a net magnetization vector. In this illustrative example, a slice in a plane along the X and Y axes, as indicated at 205, is being imaged. It should be noted that in this example, the slice has a finite thickness along the Z-axis, creating a volumetric slice 205.

To obtain images from the MRI system 100 in the traditional manner, one or more sets of RF pulses and gradient waveforms (collectively called “pulse sequences”) are selected at the data processing system 105. The data processing system 105 passes the selected pulse sequence information to the RF control unit 135 and the gradient control unit 125, which collectively generate the associated waveforms and timings for providing a sequence of pulses to perform a scan.

The sequence of RF pulses and gradient waveforms, namely the type of pulse sequence, applied may change which relaxation times have the most influence on the image characteristics. For example, T2* relaxation has a significant influence following a 90° RF pulse which is used in a gradient-echo (GRE) sequence, whereas T2 relaxation has a more significant influence following 90°-180° sequential RF pulses (also known as a spin echo sequence).

Referring now to FIG. 3, an illustrative pulse sequence 300 is shown that can be used to acquire images using the MRI system 100. Specifically, a timing diagram for the example pulse sequence is indicated. The timing diagram shows pulse or signal magnitudes, as a function of time, for the transmitted (RFt) signal, the magnetic field gradients Gx, Gy, and Gz, and the received RFx signal. An idealized pulse sequence, simplified for illustrative purposes, can contain a slice selection radio frequency pulse 310 at RFt, a slice selection gradient pulse 320 at Gz, a phase encoding gradient pulse 330 at Gy, a frequency encoding gradient pulse 340 at Gx, as well as a detected MR signal 350 at RFx. The pulses for the three gradients Gx, Gy, and Gz represent the magnitude and the duration of the magnetic field gradients that can be generated by the gradient coils 120. The slice selection pulse 310 can be generated by the transmit aspect of RF coils 130. The detected MR signal 350 can be detected by the receive aspect of the RF coils 130. In this illustrative example it will be assumed that the transmit aspect and the receive aspect of the RF coils 130 are formed by distinct coils.

The first event to occur in pulse sequence 300 can be to turn on the slice selection gradient pulse 320. The slice selection RF pulse 310 can be applied at the same time. In this illustrative example, the slice selection RF pulse 310 can be a sinc function shaped burst of RF energy. In other implementations, other RF pulse shapes and durations can be used. Once the slice selection RF pulse 310 is turned off, the slice selection gradient pulse 320 can also be turned off and a phase encoding gradient pulse 330 can be turned on. Once the phase encoding gradient pulse 330 is turned off, the frequency encoding gradient pulse 340 can be turned on and the detected MR signal 350 can be recorded. It should be noted that the shapes, magnitudes, ordering and durations of the pulses and signals shown in FIG. 3 are chosen for illustrative purposes, and that in implementations, one or more of these factors and others may be varied to achieve the desired scan results.

The pulse sequence 300 can be repeated a certain number of times or iterations, for example 256 times, to collect all the data needed to produce one image. The time between each repetition of the pulse sequence 300 can be referred to as the repetition time (TR). Moreover, the duration between the center point of the slice selection pulse 310 and the peak of detected MR signal 350 can be referred to as echo time (TE). Both the TR and the TE can be varied as appropriate for a desired scan.

To further illustrate the signal acquisition process of MRI system 100, FIG. 2 is referred to in conjunction with FIG. 3. To select a slice, the slice selection gradient pulse 320 can be applied along the Z-axis, satisfying the resonance condition for the protons located in the slice 205. Indeed, the location of the slice along the Z-axis can be determined based in part on the slice selective gradient pulse 320. Accordingly, the slice selection pulse 310, generated at the same time as the slice selection gradient pulse 320 can excite protons that are located within the slice 205 in this example. Protons located above and below the slice 205 are typically not affected by the slice selection pulse 310.

Continuing with the illustrative example, in accordance with the pulse sequence 300, a phase encoding gradient pulse 330 can be applied after the slice selection gradient pulse 320. Assuming this is applied along the Y-axis, the spins at different locations along the Y-axis can begin to precess at different Larmor frequencies. When the phase encoding gradient pulse 330 is turned off, the net magnetization vectors at different locations can precess at the same rate, but possess different phases. The phases can be determined by the duration and magnitude of the phase encoding gradient pulse 330.

Once the phase encoding gradient pulse 330 is turned off, a frequency encoding gradient pulse 340 can be turned on. In this example the frequency encoding gradient is in the X direction. The frequency encoding gradient can cause protons in the selected slice to precess at rates dependent on their X location. Accordingly, different spatial locations within the slice are now characterized by unique phase angles and precessional frequencies. RF receive coils 130 can be used to receive the detected signal 350 generated by the protons contained in the object being scanned while the frequency encoding gradient pulse 340 is turned on.

As the pulse sequence 300 is performed by the MRI system 100, the acquired signals can be stored in a temporary matrix referred to as the k-space, as shown in FIG. 4 at 400. Typically, the k-space is the collection of the detected signals measured for a scan and is in the spatial frequency domain. The k-space can be covered by frequency encoding data along the X-axis 420 (Kx) and phase encoding data along the Y-axis 430 (Ky). When all of the lines for the k-space matrix for a slice are received (at the end of the scan of a single slice, for example) the data can be mathematically processed, for example through a two-dimensional Fourier-transform, to produce a final image. Thus, the k-space can hold raw data before reconstruction of the image into the spatial domain. Typically, the k-space has the same number of rows and columns as the final image and is filled with raw data during the scan, usually one line per pulse sequence 300. For example, the first line of k-space 400, indicated at 410, is filled after the completion of the first iteration of the pulse sequence generated for scanning a slice and contains the detected signal for that pulse sequence iteration. After multiple iterations of the pulse sequence, the k-space can be filled. Each iteration of the pulse sequence may be varied slightly, so that signals for the appropriate portions of the k-space are acquired. It should be noted that based on different pulse sequences, other methods of filling the k-space are possible, such as in a spiral manner, and are contemplated.

The gradient coils 120 produce time-varying magnetic fields with a specific spatial distribution and are a typical component of MRI systems. Greater field-variation magnitudes enable faster MR imaging sequences and increased resolution. As discussed above, the maximum achievable gradient strength is characterized by the gradient efficiency. The efficiency of the gradient coils 120 can be improved through variations in the shape, size and placement of the gradient coils 120. For example, in a cylindrical implementation the primary gradient coil windings may be built at a smaller radius closer to the object in the imaging volume. Alternatively, the number of wires (winding density) can be increased.

The gradient coils 120 can have a high degree of symmetry when, for example, the object to be imaged is located at the center of the coils. Accordingly, such coils are typically referred to as symmetric gradient coils. Due to physical and geometrical constraints, for some MRI systems 100, the objects to be imaged may not be located symmetrically at the center of the gradient coils 120. Further, such coils may not even be symmetric in shape. For example, a head gradient coil may fit the head, but not the shoulders. Alternatively, there may be slots for shoulders with the coil extending above the chest and underneath the back. Coils of this type are typically known as asymmetric gradient coils.

When the gradient coils 120 are constructed, certain performance metrics can be considered. For example, the gradient coils 120 are typically constructed so as to reduce net force and torque experienced when they are energized. Net force can be characterized in each of the x, y and z directions in terms of Newtons per Ampere of current and this quantity determines the tendency for the coil to translate in space when energized. Net torque can be characterized in each of the x, y and z directions in terms of Newtons per meter per Ampere and this quantity determines the tendency for the coil to rotate when energized. Achieving force- and torque-balance is a particularly challenging problem for gradient coils 120 that are asymmetric along the longitudinal (z) dimension. For example, as shown in FIG. 5, gradient coils that are asymmetric along the longitudinal direction can have wire patterns with single spirals 510 (hereafter referred to as ‘thumbprint’ 510) for each side of the coil, an arrangement that can enable increased efficiency. In this example, two additional thumbprints 510′ are shown which form portions of the shield coil corresponding to the primary coil.

The gradient coils 120 are typically designed and constructed to lower net force and torque from such asymmetric designs. For example, in some variations, a shield coil can be used to cancel the force and/or torque of a primary coil when the two coils are part of the same rigid mechanical assembly. When the primary and the shield coil wire patterns form part of the same rigid mechanism, it is possible to get force- and/or torque-balanced implementations by using a single thumbprint for the primary coil and a single thumbprint for the shield coil, although it can also be possible to achieve force- and/or torque-balanced implementations for other patterns and numbers of thumbprints. Other considerations such as wire density and pattern can also be used to reduce net torque and force. The reduction in net torque and force experienced is made in consideration of other performance metrics limits or requirements. Thus, in some implementations, optimum force and torque-balance may be sacrificed to achieve requirements set for other performance metrics.

Efficiency is another performance metric to be considered when constructing the gradient coils 120. Efficiency can be defined as the gradient strength per unit current driven through the gradient coils 120. High efficiency aids the production of large gradient amplitudes, which in turn can allow the acquisition of higher resolution images or reduce scan times for example. Efficiency is linearly proportional to the winding density of the gradient coils 120. For example, when the winding density is doubled, the efficiency typically doubles as well. Accordingly, the gradient coils 120 are typically constructed with as high an efficiency as possible, in light of other performance metrics, including requirements set for other performance metrics. Thus, in some implementations, optimum efficiency may be sacrificed to achieve requirements set for other performance metrics. For example, a particular winding density can be chosen to obtain a desired efficiency that may be lower than the highest possible efficiency so that limits for other performance metrics can be met.

Power dissipation is yet another performance metric to be considered. Power dissipation can be determined based on power which is the resistance of the gradient coils 120 multiplied by the current squared. Accordingly, power dissipation can be a measure of the amount of heat that can be created when the gradient coils 120 are energized. Power dissipation is proportional to the square of the winding density. For example, when the winding density is doubled, the power dissipation typically quadruples. Accordingly, the gradient coils 120 are typically constructed with as low a power dissipation (and thus heat generation) as possible, in light of other performance metric requirements set. For example, a particular winding density can be chosen to obtain a desired power dissipation that may be higher than the lowest possible power dissipation so that set requirements for other performance metrics can be met.

Energy is a further performance metric that can be considered when constructing the gradient coils 120. Energy can be defined as the inductance of the gradient coils 120 multiplied by the current squared multiplied by 0.5. This metric can be a measure of how fast the gradient coils 120 can be switched on or off. Lower energy typically implies faster switching rates. Energy, similar to power dissipation is proportional with the square of the winding density. For example, when the winding density is doubled, the energy typically quadruples. Accordingly, the gradient coils 120 are typically constructed with as low an energy (fastest switching) as possible, in light of other performance metric requirements. For example, a particular winding density can be chosen to obtain a desired energy that may be higher than the lowest possible energy so that the requirements set for other performance metrics can be met.

Gradient field-shape metric is a further performance metric. Magnetic field gradient linearity and uniformity is typically a primary consideration when implementing the gradient coils 120. Gradient field-shape metric is a measure of how well the field that the gradient coils 120 produces matches a target gradient field, which in the example MRI system 100 has a linear and uniform spatial gradient. There are many ways that this gradient metric can be defined. An example definition is the sum of the squared difference between the field that is produced by the gradient coils 120 and the target gradient field over a set of positions in a volume of interest. Based on this definition, the gradient field-shape metric is lowered, to the extent possible, in light of other performance metric requirements specified. For example, a particular winding pattern can be chosen to obtain a particular gradient linearity metric that may be higher than the lowest possible gradient linearity metric so that specified requirements for other performance metrics can be met.

Other performance metrics that will now occur to a person of skill, such as eddy-field and others can also be defined in a similar manner.

To achieve the performance metric limits associated with different performance metric requirements, a representation of the current density for the gradient coils 120 over the surface where the gradient coils 120 are to reside (for example, a cylinder) can be generated. This representation can be analytic, usually incorporating some sort of basis representation for the given geometry. For example, where the gradient coils 120 are to reside on a cylinder, cylindrical harmonics can be used as the basis representation. Alternatively, the representation can be numerical. For example, the current density for the gradient coils 120 can be based on current elements over a finite triangular mesh. In a boundary element method (BEM) approach to coil design, for example, any surface on which electrical current can flow can be approximated or represented by a collection of triangular elements that form a mesh over the whole surface. Within each element is contained information that describes the direction and magnitude of the electrical current density. A step in the BEM, accordingly, is the discretization of a surface geometry into a finite mesh composed of triangular elements. The triangular elements are hereinafter referred to as elements and the vertices of these elements are hereinafter referred to as nodes. FIG. 6 shows an example cylindrical surface onto which the gradient coils 120 are to be placed, discretized into a fine mesh composed of triangles.

In practice, in accordance with the BEM, the current density pattern over a two dimensional surface can be represented in an indirect manner in the form of a scalar stream function. The stream function can be represented as a piece-wise linear (or higher order) function over the surface geometry on which the gradient coils 120 are to be placed. The stream function can consist of a single scalar value for each node in the mesh and when all of the nodes are considered together, the stream function can be transformed to find the direction and magnitude of the current density in each triangular element.

In one implementation, a stream function, ψ(r), residing within the surface of elements with corresponding current density J(r) can be defined, where r represents the position on the mesh. The stream function can be approximated by a weighted sum of basis functions for each node n as:

$\begin{matrix} {{\psi(r)} = {\sum\limits_{n = 1}^{N}{I_{n}{\psi_{n}(r)}}}} & \left( {{equation}\mspace{14mu} 1.1} \right) \end{matrix}$

In equation 1.1, I_(n) is the weighting coefficient for the basis function ψ_(n)(r) of node n. With this approximation, the current density for the stream function can be represented as a sum of current density basis functions, defined as:

$\begin{matrix} {{J(r)} = {\nabla{\times \left\lbrack {{\psi(r)}{n(r)}} \right\rbrack}}} & \left( {{equation}\mspace{14mu} 1.2} \right) \\ {{J(r)} \approx {\sum\limits_{n = 1}^{N}{I_{n}{\nabla{\times \left\lbrack {{\psi_{n}(r)}{n(r)}} \right\rbrack}}}}} & \left( {{equation}\mspace{14mu} 1.3} \right) \\ {{J(r)} \approx {\sum\limits_{n = 1}^{N}{I_{n}{J_{n}(r)}}}} & \left( {{equation}\mspace{14mu} 1.4} \right) \\ {{{J_{n}(r)} \approx {\sum\limits_{k = 1}^{K}v_{nk}}} = {\sum\limits_{k = 1}^{K}\frac{e_{nk}}{2A_{k}}}} & \left( {{equation}\mspace{14mu} 1.5} \right) \end{matrix}$

In equations 1.2 through 1.5, n(r) is the outward pointing normal of the surface, K is the number of triangles surrounding node n, A_(k) is the area of triangular element k associated with node n, and e_(nk) is the vector that opposes node n within triangular element k.

The current density representation (or the stream functions) can be used to produce a pattern of current density that achieves the set requirements for performance metric such as balancing of matching magnetic field targets and having low power dissipation while at the same time satisfying specified requirements for net torque and/or force. For example, performance metrics that can be described by a current density, including for example, the gradient field-shape metric, dissipative power, energy, force and torque can be described based on various performance metric functions.

To find the stream function and corresponding current density representation that achieves the specified requirements set for performance metrics, a performance functional can be formed using the performance metrics as functions. In some implementations, the performance metric functions can include weighting parameters. In other implementations, performance metric functions may be set as constraints on the performance functional. A constraint can be set in the form of a single value (i.e. constrained to zero) or a range of values that are acceptable for that performance function. In yet further variations, the above discussed approaches to satisfying the performance metric requirements may be combined, for example some performance metrics being used to constrain the performance functional and other performance metrics including weighting parameters.

Once the performance functional is formed, it can be minimized or optimized to produce a current density pattern that achieves the specified gradient coil performance metric constraints. The minimization can be based on various techniques such as least-squares matrix inversion, analytic formulae or an iterative solver. For example, where one or more performance metric functions include weighting parameters, the competing performance metrics can be balanced simultaneously, to achieve the desired performance metric requirements such as low power dissipation and desired field shape by finding a set of parameters that minimizes the performance functional. As a further example, in implementations where one or more performance metrics are set as constraints, constrained optimization can be used to find the desired performance metric requirements. In variations, the solution of the performance functional itself can be set to be constrained to a certain desired range. If not in range, performance metrics or weighting parameters can be changed, for example, to obtain a different solution. This process can be repeated iteratively until the obtained solution is within the range of acceptable design goals. Example goals include minimum conductor separation, maximum power deposition per unit area, maximum force on a given component and others.

The resulting current density pattern obtained by minimizing or optimizing the performance functional can be contoured to obtain a wire pattern, which is a discrete number of current paths that approximates the current density represented by the stream function. FIGS. 7(a) and 7(b) display a stream function and corresponding wire pattern respectively after contouring for a transverse gradient coil implemented over a cylindrical surface. The choice of number of contours (and thus the coil wire density) can also be based on the performance metric weightings and constraints since some of the performance metric weightings and constraints may be related to wire density, for example, a constraint to enforce a certain minimum wire separation.

The use of the processes above allows any desired surface shape to be used over which an electromagnet can be implemented. The discretization of the stream function is dependent on the shape of the finite elements making up the mesh rather than the shape of the final surface. However, the mesh surfaces are typically non-intersecting.

In some implementations, torque or force exerted on an electromagnet as a result of non-uniformities in the main magnetic field within which an electromagnet is placed can also be minimized. Referring to FIG. 8, an illustrative example is shown of is a non-uniform external magnetic field of the main field magnet 110 as a function of z positions and radial (r) positions in meters over the range of locations occupied by the gradient coils 120. The top field surface is the z component of the main magnetic field and the bottom field surface shows the radial (r) component of the main magnetic field. Such non-uniform external magnetic fields can cause significant torque and force on electromagnets such as the gradient coils 120 placed within it. Accordingly, a performance metric function that accounts for external torque and/or external force exerted on an electromagnet due to a non-uniform field external to the electromagnet, such as the main magnetic field generated by the main field magnet 110, can be included in the performance functional. The performance metric functional can then be optimized with the requirements specified for the external torque and/or external force resulting from the non-uniform external magnetic field. For example, weighting parameters can be associated with the external force and the external torque performance metrics. Alternatively, these performance metrics can be constrained to a specified requirement such as no external torque and/or external force or a value close to zero. Alternatively, a range of values can be specified as acceptable by the requirements.

In variations, the position of an electromagnet within the external magnetic field can also be a specified requirement for the design and manufacture of the electromagnet. For example, external force and external torque can be balanced at exactly one position. In such circumstances, the electromagnet may experience significant forces if moved by a small distance in one or more directions. Furthermore, in some cases, the one position where the balance is achieved can in fact represent an unstable equilibrium and the electromagnet may experience stronger torque and/or force in the direction of displacement as the displacement increases (thus risking that the electromagnet can turn into a projectile risk). Accordingly, when the external torque and external force are balanced for a single location, the electromagnet is placed in position with high precision. In further variations the external torque and the external force can be balanced for a range of locations. For example, the location may be constrained to a range of positions. Accordingly, the optimization can occur for a range of positions of the electromagnet within the external magnetic field. Thus, the precision with which the electromagnet is positioned within the external magnetic field can be relaxed.

Referring to FIG. 9 a method of manufacturing gradient coils 120 is shown at 900. At 1010, a volume of interest where the gradient field will be generated is chosen. This typically corresponds to a volume within the main magnet 110. At 920, the shape of the surface on which the gradient coils 120 are to be placed are identified, which in this example is a cylinder within the bore of the main magnet 110. At 930, representations of the surfaces are formed. For example, the cylindrical surface is triangulated and a representation formed. At 940, performance metric set limits are identified. In this example, the performance metrics are the gradient linearity metric and the external force and external torque metrics representing force and torque caused by a non-uniform external field within which the electromagnet is placed. At 950 a performance functional is formed and optimized. The performance functional in this example includes performance metric functions for the gradient linearity metric and the externally caused torque and force metrics. At 960 the current density is computed based on the minimized performance functional and coil windings are obtained based on a contouring of the current density pattern.

The gradient coils 120 manufactured and operated in accordance with the above described methods can be applied to any application or geometry of MRI systems. In variations, the above discussed methods can also be applied to the design, manufacture and operation of electromagnets besides gradient coils. For example, correction coils 140 can also be designed and manufactured in accordance with the above described processes. As a further example, field-shifting coils used in delta relaxation enhanced magnetic resonance imaging can also be designed, manufactured and operated in accordance with the above described processes.

The above-described embodiments are intended to be examples and alterations and modifications may be effected thereto, by those of skill in the art, without departing from the scope which is defined solely by the claims appended hereto. For example, methods, systems and embodiments discussed can be varied and combined, in full or in part. 

We claim:
 1. A method of manufacturing electromagnet coils for use in a magnetic resonance imaging (MRI) system, the electromagnet coils being located in a non-homogeneous external magnetic field, the method comprising: forming a coil representation of a coil surface for the electromagnet coils; setting a plurality of performance metric requirements for a plurality of performance metrics for the electromagnet coils, the plurality of performance metrics including a magnetic field-shape metric and at least one of an external torque metric and an external force metric, the external torque metric and the external force metric being based, respectively, at least in part on a torque and a force exerted on the electromagnet coil by the non-homogeneous external magnetic field; forming a performance functional, based on the coil representation and the performance metrics, for generating a current density pattern over the coil surface; optimizing the performance functional based on the performance metric requirements; generating a current density pattern over the coil surface based on the optimized performance functional; and obtaining coil windings for the electromagnet coils from the current density pattern, wherein the optimizing is performed for a plurality of positions of the electromagnet coils with respect to the non-homogeneous external magnetic field.
 2. The method of claim 1, wherein the current density pattern is based on a stream function.
 3. The method of claim 1, wherein the magnetic field-shape metric further comprises a target magnetic field and wherein the optimizing of the performance functional further comprises minimizing the difference between the target magnetic field and a predicted magnetic field generated based on the performance functional.
 4. The method of claim 1, wherein the performance metrics can further comprise at least one of: a dissipative power metric, an energy metric and an eddy-field metric.
 5. The method of claim 1, further comprising: forming performance metric functions based on performance metrics, and wherein the performance functional is formed in part from the performance metric functions.
 6. The method of claim 1, wherein the coil representation for the electromagnet coils is based on a boundary element method.
 7. The method of claim 1, wherein the coil surface is cylindrical.
 8. The method of claim 1, wherein the electromagnet coils are one of field-shifting coils, gradient coils and correction coils.
 9. The method of claim 1, wherein the MRI system further comprises a main magnet and wherein the non-homogeneous external magnetic field is generated by the main magnet.
 10. The method of claim 1, the optimizing being further constrained by a minimum conductor separation of the obtained coils.
 11. An MRI system manufactured in accordance with the method of claim
 1. 12. The method of claim 1, wherein forming said coil representation comprises forming an asymmetric coil surface for the electromagnet coils.
 13. The method of claim 1, wherein the plurality of performance metrics associated with the external force metric and external torque metric can be constraints. 